Question

Which of these equations has a graph that is tangent to the x-axis at one of its intercepts? Choose all the polynomials that have this property.

y = x2 + 6x + 9
y = –x3
y = (x + 2)(x + 6)2
y = (x – 5)(x + 3)(x + 1)(x – 5)
y = x4

Answer 1

i think y=x2+6x+9 hope this helps

Answer 2

`y=x^(2)+6x+9`

`y=-x^(3)`

`y=(x+2)(x+6)^(2)`

`y=(x-5)(x+3)(x+1)(x-5)`

`y=x^(4)`

Explanation:

we know that

If the graph is tangent to the x-axis at one of its intercepts

then

the vertex of the graph or the inflection point of the graph lie on the x-axis

using a graphing tool

Verify each case

case A)
`y=x^(2)+6x+9`

The case A) has a graph that is tangent to the x-axis at one of its intercepts

case B)
`y=-x^(3)`

The case B) has a graph that is tangent to the x-axis at one of its intercepts

case C)
`y=(x+2)(x+6)^(2)`

The case C) has a graph that is tangent to the x-axis at one of its intercepts

case D)
`y=(x-5)(x+3)(x+1)(x-5)`

The case D) has a graph that is tangent to the x-axis at one of its intercepts

case E)
`y=x^(4)`

The case E) has a graph that is tangent to the x-axis at one of its intercepts